Optimal. Leaf size=45 \[ \frac{18 x^2}{125}-\frac{264 x}{625}-\frac{682}{3125 (5 x+3)}-\frac{121}{6250 (5 x+3)^2}+\frac{829 \log (5 x+3)}{3125} \]
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Rubi [A] time = 0.0194944, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ \frac{18 x^2}{125}-\frac{264 x}{625}-\frac{682}{3125 (5 x+3)}-\frac{121}{6250 (5 x+3)^2}+\frac{829 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (2+3 x)^2}{(3+5 x)^3} \, dx &=\int \left (-\frac{264}{625}+\frac{36 x}{125}+\frac{121}{625 (3+5 x)^3}+\frac{682}{625 (3+5 x)^2}+\frac{829}{625 (3+5 x)}\right ) \, dx\\ &=-\frac{264 x}{625}+\frac{18 x^2}{125}-\frac{121}{6250 (3+5 x)^2}-\frac{682}{3125 (3+5 x)}+\frac{829 \log (3+5 x)}{3125}\\ \end{align*}
Mathematica [A] time = 0.0154481, size = 42, normalized size = 0.93 \[ \frac{\frac{5 \left (4500 x^4-7800 x^3-23760 x^2-17564 x-4277\right )}{(5 x+3)^2}+1658 \log (5 x+3)}{6250} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 36, normalized size = 0.8 \begin{align*} -{\frac{264\,x}{625}}+{\frac{18\,{x}^{2}}{125}}-{\frac{121}{6250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{682}{9375+15625\,x}}+{\frac{829\,\ln \left ( 3+5\,x \right ) }{3125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10207, size = 49, normalized size = 1.09 \begin{align*} \frac{18}{125} \, x^{2} - \frac{264}{625} \, x - \frac{11 \,{\left (620 \, x + 383\right )}}{6250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{829}{3125} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.5152, size = 163, normalized size = 3.62 \begin{align*} \frac{22500 \, x^{4} - 39000 \, x^{3} - 71100 \, x^{2} + 1658 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 30580 \, x - 4213}{6250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.116527, size = 36, normalized size = 0.8 \begin{align*} \frac{18 x^{2}}{125} - \frac{264 x}{625} - \frac{6820 x + 4213}{156250 x^{2} + 187500 x + 56250} + \frac{829 \log{\left (5 x + 3 \right )}}{3125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.74329, size = 43, normalized size = 0.96 \begin{align*} \frac{18}{125} \, x^{2} - \frac{264}{625} \, x - \frac{11 \,{\left (620 \, x + 383\right )}}{6250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{829}{3125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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